Question:
The relation $R = \{(4,4), (4,5), (5, 7), (4, 8), (5, 5), (7, 8), (7, 7), (7, 5), (8, 8), (8, 7), (8, 5), (9, 9)\}$ on the set $A=\{4,5,7,8,9\}$ is ________.
The relation $R = \{(4,4), (4,5), (5, 7), (4, 8), (5, 5), (7, 8), (7, 7), (7, 5), (8, 8), (8, 7), (8, 5), (9, 9)\}$ on the set $A=\{4,5,7,8,9\}$ is ________.
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Reflexive means every element is related to itself.
Updated On: Jun 26, 2026
- transitive
- symmetric
- reflexive
- equivalence relation
- a function
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Concept
A relation $R$ on set $A$ is reflexive if $(a, a) \in R$ for every $a \in A$.
Step 2: Meaning
The set $A$ contains elements $\{4, 5, 7, 8, 9\}$.
Step 3: Analysis
Checking for reflexivity: $(4,4), (5,5), (7,7), (8,8),$ and $(9,9)$ are all present in $R$.
Step 4: Conclusion
Since all identity pairs for set $A$ exist in $R$, the relation is reflexive. Final Answer: (C)
A relation $R$ on set $A$ is reflexive if $(a, a) \in R$ for every $a \in A$.
Step 2: Meaning
The set $A$ contains elements $\{4, 5, 7, 8, 9\}$.
Step 3: Analysis
Checking for reflexivity: $(4,4), (5,5), (7,7), (8,8),$ and $(9,9)$ are all present in $R$.
Step 4: Conclusion
Since all identity pairs for set $A$ exist in $R$, the relation is reflexive. Final Answer: (C)
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